Henry Cotton was the son of Colonel Vere Egerton Cotton and his wife Elfreda (née Moore). On 18 June 1955, he married Elizabeth Peard, daughter of Clifford James Peard, DSO, JP.[3] They had one daughter, Catherine and one son, Timothy. Catherine (Kate) Cotton had one daughter, Natalie Psillou.
In 1992, Henry Cotton was appointed the First Chancellor of Liverpool John Moores University after it gained university status from being a polytechnic. The institution however goes as far back as 1823 to its foundation as the Liverpool Mechanics' School of Arts, entitling it to make a claim in the third-oldest university in England debate. He served in office until his death in 1993. He was succeeded by John Moores, Jr, CBE who was the son of Sir John Moores after whom the university is named.
A statue of Henry Cotton inscribed "Henry Egerton Cotton Esq, (1929-1993) LL.D, JP, First Chancellor of the University, 1992-1993" has been erected outside the Henry Cotton Building named in his honour, on the university's City Campus in Liverpool.[4]